Fuchsian系统的分类及其连接问题
Classification of Fuchsian systems and their connection problem
摘要：
我们回顾Deligne-Simpson问题，一个中卷积的组合结构，以及它们与Crawley-Boevey提出的Kac-Moody根系的关系。我们用例子说明了中卷积将具有固定数目的辅助参数的Fuchsian系统变换为谱型在有限集的基本系统，并给出了无模Fuchsian微分方程解的显式联系公式.
英文摘要：
We review the Deligne-Simpson problem, a combinatorial structure of middle convolutions and their relation to a Kac-Moody root system discoverd by Crawley-Boevey. We show with examples that middle convolutions transform the Fuchsian systems with a fixed number of accessory parameters into fundamental systems whose spectral type is in a finite set and we give an explicit connection formula for solutions of Fuchsian differential equations without moduli.
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